Sélection de variables dans les modèles additifs avec des estimateurs en plusieurs étapes

Abstract : In this document, we present some multi-step nonparametric estimators used for additive models, whose components are approximated by their series developments in B-splines. We assume that the number of covariates can be larger than the number of observations, but that the number of influent covariates is less than the number of observations. In our work, the fact that a covariate has a significant effect does not mean that the norm of the corresponding component is bounded below by a constant positive bound as it is usually assumed in this context, since we only request that norms of significant components to be bounded below by a bound that may decrease to zero at an appropriate speed. We focus on selection and estimation of sparse additive models in this asymptotic context. Our multi-step estimators combine least squares or P-Splines estimators with Group LASSO. We discuss several model selection criteria (AIC, GCV or BIC) and we establish the proofs of selection and estimation consistency of one of our estimators. The behaviour of the resulting estimators is illustrated via simulations.
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Submitted on : Thursday, February 12, 2015 - 3:35:13 PM
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Anestis Antoniadis, Yannig Goude, Jean-Michel Poggi, Vincent Thouvenot. Sélection de variables dans les modèles additifs avec des estimateurs en plusieurs étapes. [Rapport Technique] Université d'Orsay; EDF R&D; Université Joseph Fourier; Université Cap Town; Université Paris Descartes. 2015. ⟨hal-01116100⟩

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